Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.9203 | −1.01295 | −0.506473 | − | 0.862256i | \(-0.669051\pi\) | ||||
−0.506473 | + | 0.862256i | \(0.669051\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 13.3420 | 0.0260586 | ||||||||
\(5\) | 1892.34 | 1.35405 | 0.677023 | − | 0.735962i | \(-0.263270\pi\) | ||||
0.677023 | + | 0.735962i | \(0.263270\pi\) | |||||||
\(6\) | 1856.55 | 0.584824 | ||||||||
\(7\) | −10585.6 | −1.66638 | −0.833189 | − | 0.552989i | \(-0.813487\pi\) | ||||
−0.833189 | + | 0.552989i | \(0.813487\pi\) | |||||||
\(8\) | 11429.4 | 0.986550 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −43373.0 | −1.37157 | ||||||||
\(11\) | −11310.1 | −0.232917 | −0.116458 | − | 0.993196i | \(-0.537154\pi\) | ||||
−0.116458 | + | 0.993196i | \(0.537154\pi\) | |||||||
\(12\) | −1080.70 | −0.0150449 | ||||||||
\(13\) | 75180.1 | 0.730059 | 0.365030 | − | 0.930996i | \(-0.381059\pi\) | ||||
0.365030 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(14\) | 242625. | 1.68795 | ||||||||
\(15\) | −153279. | −0.781759 | ||||||||
\(16\) | −268797. | −1.02538 | ||||||||
\(17\) | 10052.0 | 0.0291897 | 0.0145949 | − | 0.999893i | \(-0.495354\pi\) | ||||
0.0145949 | + | 0.999893i | \(0.495354\pi\) | |||||||
\(18\) | −150380. | −0.337648 | ||||||||
\(19\) | 190115. | 0.334677 | 0.167338 | − | 0.985900i | \(-0.446483\pi\) | ||||
0.167338 | + | 0.985900i | \(0.446483\pi\) | |||||||
\(20\) | 25247.5 | 0.0352845 | ||||||||
\(21\) | 857432. | 0.962083 | ||||||||
\(22\) | 259232. | 0.235932 | ||||||||
\(23\) | −1.70428e6 | −1.26989 | −0.634944 | − | 0.772559i | \(-0.718977\pi\) | ||||
−0.634944 | + | 0.772559i | \(0.718977\pi\) | |||||||
\(24\) | −925782. | −0.569585 | ||||||||
\(25\) | 1.62781e6 | 0.833441 | ||||||||
\(26\) | −1.72315e6 | −0.739510 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −141233. | −0.0434234 | ||||||||
\(29\) | −4.88265e6 | −1.28193 | −0.640966 | − | 0.767570i | \(-0.721466\pi\) | ||||
−0.640966 | + | 0.767570i | \(0.721466\pi\) | |||||||
\(30\) | 3.51321e6 | 0.791879 | ||||||||
\(31\) | 1.15157e6 | 0.223955 | 0.111978 | − | 0.993711i | \(-0.464281\pi\) | ||||
0.111978 | + | 0.993711i | \(0.464281\pi\) | |||||||
\(32\) | 309062. | 0.0521040 | ||||||||
\(33\) | 916122. | 0.134475 | ||||||||
\(34\) | −230394. | −0.0295676 | ||||||||
\(35\) | −2.00315e7 | −2.25635 | ||||||||
\(36\) | 87536.8 | 0.00868619 | ||||||||
\(37\) | 1.23793e7 | 1.08590 | 0.542949 | − | 0.839766i | \(-0.317308\pi\) | ||||
0.542949 | + | 0.839766i | \(0.317308\pi\) | |||||||
\(38\) | −4.35750e6 | −0.339009 | ||||||||
\(39\) | −6.08959e6 | −0.421500 | ||||||||
\(40\) | 2.16283e7 | 1.33583 | ||||||||
\(41\) | 2.65126e7 | 1.46529 | 0.732647 | − | 0.680608i | \(-0.238285\pi\) | ||||
0.732647 | + | 0.680608i | \(0.238285\pi\) | |||||||
\(42\) | −1.96526e7 | −0.974538 | ||||||||
\(43\) | −3.02092e6 | −0.134751 | −0.0673753 | − | 0.997728i | \(-0.521462\pi\) | ||||
−0.0673753 | + | 0.997728i | \(0.521462\pi\) | |||||||
\(44\) | −150900. | −0.00606948 | ||||||||
\(45\) | 1.24156e7 | 0.451349 | ||||||||
\(46\) | 3.90626e7 | 1.28633 | ||||||||
\(47\) | 1.63487e7 | 0.488700 | 0.244350 | − | 0.969687i | \(-0.421425\pi\) | ||||
0.244350 | + | 0.969687i | \(0.421425\pi\) | |||||||
\(48\) | 2.17726e7 | 0.592003 | ||||||||
\(49\) | 7.17008e7 | 1.77681 | ||||||||
\(50\) | −3.73101e7 | −0.844230 | ||||||||
\(51\) | −814208. | −0.0168527 | ||||||||
\(52\) | 1.00305e6 | 0.0190243 | ||||||||
\(53\) | 8.99069e7 | 1.56513 | 0.782567 | − | 0.622567i | \(-0.213910\pi\) | ||||
0.782567 | + | 0.622567i | \(0.213910\pi\) | |||||||
\(54\) | 1.21808e7 | 0.194941 | ||||||||
\(55\) | −2.14026e7 | −0.315380 | ||||||||
\(56\) | −1.20987e8 | −1.64396 | ||||||||
\(57\) | −1.53993e7 | −0.193226 | ||||||||
\(58\) | 1.11912e8 | 1.29853 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −2.04505e6 | −0.0203715 | ||||||||
\(61\) | −7.84701e6 | −0.0725638 | −0.0362819 | − | 0.999342i | \(-0.511551\pi\) | ||||
−0.0362819 | + | 0.999342i | \(0.511551\pi\) | |||||||
\(62\) | −2.63943e7 | −0.226855 | ||||||||
\(63\) | −6.94520e7 | −0.555459 | ||||||||
\(64\) | 1.30540e8 | 0.972601 | ||||||||
\(65\) | 1.42266e8 | 0.988534 | ||||||||
\(66\) | −2.09978e7 | −0.136216 | ||||||||
\(67\) | −1.02865e7 | −0.0623633 | −0.0311816 | − | 0.999514i | \(-0.509927\pi\) | ||||
−0.0311816 | + | 0.999514i | \(0.509927\pi\) | |||||||
\(68\) | 134113. | 0.000760643 0 | ||||||||
\(69\) | 1.38047e8 | 0.733170 | ||||||||
\(70\) | 4.59128e8 | 2.28556 | ||||||||
\(71\) | 7.77522e7 | 0.363120 | 0.181560 | − | 0.983380i | \(-0.441885\pi\) | ||||
0.181560 | + | 0.983380i | \(0.441885\pi\) | |||||||
\(72\) | 7.49884e7 | 0.328850 | ||||||||
\(73\) | 9.47922e7 | 0.390679 | 0.195339 | − | 0.980736i | \(-0.437419\pi\) | ||||
0.195339 | + | 0.980736i | \(0.437419\pi\) | |||||||
\(74\) | −2.83738e8 | −1.09995 | ||||||||
\(75\) | −1.31853e8 | −0.481187 | ||||||||
\(76\) | 2.53651e6 | 0.00872120 | ||||||||
\(77\) | 1.19724e8 | 0.388128 | ||||||||
\(78\) | 1.39575e8 | 0.426956 | ||||||||
\(79\) | 2.02657e8 | 0.585382 | 0.292691 | − | 0.956207i | \(-0.405449\pi\) | ||||
0.292691 | + | 0.956207i | \(0.405449\pi\) | |||||||
\(80\) | −5.08655e8 | −1.38841 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −6.07678e8 | −1.48426 | ||||||||
\(83\) | −5.81838e8 | −1.34571 | −0.672854 | − | 0.739776i | \(-0.734932\pi\) | ||||
−0.672854 | + | 0.739776i | \(0.734932\pi\) | |||||||
\(84\) | 1.14398e7 | 0.0250705 | ||||||||
\(85\) | 1.90217e7 | 0.0395243 | ||||||||
\(86\) | 6.92405e7 | 0.136495 | ||||||||
\(87\) | 3.95495e8 | 0.740123 | ||||||||
\(88\) | −1.29268e8 | −0.229784 | ||||||||
\(89\) | −1.16553e9 | −1.96910 | −0.984551 | − | 0.175100i | \(-0.943975\pi\) | ||||
−0.984551 | + | 0.175100i | \(0.943975\pi\) | |||||||
\(90\) | −2.84570e8 | −0.457192 | ||||||||
\(91\) | −7.95825e8 | −1.21655 | ||||||||
\(92\) | −2.27385e7 | −0.0330914 | ||||||||
\(93\) | −9.32769e7 | −0.129301 | ||||||||
\(94\) | −3.74717e8 | −0.495026 | ||||||||
\(95\) | 3.59762e8 | 0.453168 | ||||||||
\(96\) | −2.50340e7 | −0.0300823 | ||||||||
\(97\) | −1.43073e9 | −1.64091 | −0.820456 | − | 0.571709i | \(-0.806281\pi\) | ||||
−0.820456 | + | 0.571709i | \(0.806281\pi\) | |||||||
\(98\) | −1.64341e9 | −1.79981 | ||||||||
\(99\) | −7.42059e7 | −0.0776390 | ||||||||
\(100\) | 2.17183e7 | 0.0217183 | ||||||||
\(101\) | 1.67737e9 | 1.60392 | 0.801958 | − | 0.597381i | \(-0.203792\pi\) | ||||
0.801958 | + | 0.597381i | \(0.203792\pi\) | |||||||
\(102\) | 1.86619e7 | 0.0170709 | ||||||||
\(103\) | −2.83740e8 | −0.248401 | −0.124201 | − | 0.992257i | \(-0.539637\pi\) | ||||
−0.124201 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(104\) | 8.59265e8 | 0.720239 | ||||||||
\(105\) | 1.62255e9 | 1.30271 | ||||||||
\(106\) | −2.06070e9 | −1.58539 | ||||||||
\(107\) | 1.88662e9 | 1.39142 | 0.695710 | − | 0.718322i | \(-0.255090\pi\) | ||||
0.695710 | + | 0.718322i | \(0.255090\pi\) | |||||||
\(108\) | −7.09048e6 | −0.00501497 | ||||||||
\(109\) | 2.26717e9 | 1.53838 | 0.769192 | − | 0.639017i | \(-0.220659\pi\) | ||||
0.769192 | + | 0.639017i | \(0.220659\pi\) | |||||||
\(110\) | 4.90555e8 | 0.319463 | ||||||||
\(111\) | −1.00272e9 | −0.626943 | ||||||||
\(112\) | 2.84537e9 | 1.70867 | ||||||||
\(113\) | 3.82869e8 | 0.220901 | 0.110450 | − | 0.993882i | \(-0.464771\pi\) | ||||
0.110450 | + | 0.993882i | \(0.464771\pi\) | |||||||
\(114\) | 3.52958e8 | 0.195727 | ||||||||
\(115\) | −3.22507e9 | −1.71949 | ||||||||
\(116\) | −6.51443e7 | −0.0334053 | ||||||||
\(117\) | 4.93257e8 | 0.243353 | ||||||||
\(118\) | 2.77734e8 | 0.131874 | ||||||||
\(119\) | −1.06406e8 | −0.0486411 | ||||||||
\(120\) | −1.75189e9 | −0.771244 | ||||||||
\(121\) | −2.23003e9 | −0.945750 | ||||||||
\(122\) | 1.79856e8 | 0.0735032 | ||||||||
\(123\) | −2.14752e9 | −0.845988 | ||||||||
\(124\) | 1.53642e7 | 0.00583596 | ||||||||
\(125\) | −6.15598e8 | −0.225529 | ||||||||
\(126\) | 1.59186e9 | 0.562650 | ||||||||
\(127\) | −1.91749e8 | −0.0654057 | −0.0327029 | − | 0.999465i | \(-0.510412\pi\) | ||||
−0.0327029 | + | 0.999465i | \(0.510412\pi\) | |||||||
\(128\) | −3.15027e9 | −1.03730 | ||||||||
\(129\) | 2.44694e8 | 0.0777983 | ||||||||
\(130\) | −3.26079e9 | −1.00133 | ||||||||
\(131\) | −1.24390e8 | −0.0369034 | −0.0184517 | − | 0.999830i | \(-0.505874\pi\) | ||||
−0.0184517 | + | 0.999830i | \(0.505874\pi\) | |||||||
\(132\) | 1.22229e7 | 0.00350422 | ||||||||
\(133\) | −2.01248e9 | −0.557698 | ||||||||
\(134\) | 2.35769e8 | 0.0631706 | ||||||||
\(135\) | −1.00567e9 | −0.260586 | ||||||||
\(136\) | 1.14888e8 | 0.0287971 | ||||||||
\(137\) | −2.59462e9 | −0.629261 | −0.314630 | − | 0.949214i | \(-0.601881\pi\) | ||||
−0.314630 | + | 0.949214i | \(0.601881\pi\) | |||||||
\(138\) | −3.16407e9 | −0.742661 | ||||||||
\(139\) | −1.74072e9 | −0.395514 | −0.197757 | − | 0.980251i | \(-0.563366\pi\) | ||||
−0.197757 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(140\) | −2.67260e8 | −0.0587973 | ||||||||
\(141\) | −1.32424e9 | −0.282151 | ||||||||
\(142\) | −1.78211e9 | −0.367821 | ||||||||
\(143\) | −8.50298e8 | −0.170043 | ||||||||
\(144\) | −1.76358e9 | −0.341793 | ||||||||
\(145\) | −9.23962e9 | −1.73579 | ||||||||
\(146\) | −2.17267e9 | −0.395736 | ||||||||
\(147\) | −5.80776e9 | −1.02584 | ||||||||
\(148\) | 1.65165e8 | 0.0282969 | ||||||||
\(149\) | −7.64215e9 | −1.27021 | −0.635107 | − | 0.772424i | \(-0.719044\pi\) | ||||
−0.635107 | + | 0.772424i | \(0.719044\pi\) | |||||||
\(150\) | 3.02211e9 | 0.487417 | ||||||||
\(151\) | −1.22281e10 | −1.91410 | −0.957048 | − | 0.289930i | \(-0.906368\pi\) | ||||
−0.957048 | + | 0.289930i | \(0.906368\pi\) | |||||||
\(152\) | 2.17290e9 | 0.330175 | ||||||||
\(153\) | 6.59509e7 | 0.00972991 | ||||||||
\(154\) | −2.74412e9 | −0.393152 | ||||||||
\(155\) | 2.17915e9 | 0.303246 | ||||||||
\(156\) | −8.12472e7 | −0.0109837 | ||||||||
\(157\) | 5.85575e9 | 0.769190 | 0.384595 | − | 0.923085i | \(-0.374341\pi\) | ||||
0.384595 | + | 0.923085i | \(0.374341\pi\) | |||||||
\(158\) | −4.64497e9 | −0.592961 | ||||||||
\(159\) | −7.28246e9 | −0.903630 | ||||||||
\(160\) | 5.84850e8 | 0.0705512 | ||||||||
\(161\) | 1.80408e10 | 2.11611 | ||||||||
\(162\) | −9.86645e8 | −0.112549 | ||||||||
\(163\) | −1.43432e9 | −0.159148 | −0.0795742 | − | 0.996829i | \(-0.525356\pi\) | ||||
−0.0795742 | + | 0.996829i | \(0.525356\pi\) | |||||||
\(164\) | 3.53731e8 | 0.0381835 | ||||||||
\(165\) | 1.73361e9 | 0.182085 | ||||||||
\(166\) | 1.33359e10 | 1.36313 | ||||||||
\(167\) | −1.81042e10 | −1.80117 | −0.900584 | − | 0.434683i | \(-0.856861\pi\) | ||||
−0.900584 | + | 0.434683i | \(0.856861\pi\) | |||||||
\(168\) | 9.79994e9 | 0.949143 | ||||||||
\(169\) | −4.95245e9 | −0.467014 | ||||||||
\(170\) | −4.35983e8 | −0.0400359 | ||||||||
\(171\) | 1.24735e9 | 0.111559 | ||||||||
\(172\) | −4.03051e7 | −0.00351141 | ||||||||
\(173\) | −1.89193e9 | −0.160582 | −0.0802910 | − | 0.996771i | \(-0.525585\pi\) | ||||
−0.0802910 | + | 0.996771i | \(0.525585\pi\) | |||||||
\(174\) | −9.06488e9 | −0.749705 | ||||||||
\(175\) | −1.72313e10 | −1.38883 | ||||||||
\(176\) | 3.04013e9 | 0.238828 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 2.67143e10 | 1.99459 | ||||||||
\(179\) | −6.69832e9 | −0.487671 | −0.243836 | − | 0.969817i | \(-0.578406\pi\) | ||||
−0.243836 | + | 0.969817i | \(0.578406\pi\) | |||||||
\(180\) | 1.65649e8 | 0.0117615 | ||||||||
\(181\) | −4.76974e9 | −0.330325 | −0.165162 | − | 0.986266i | \(-0.552815\pi\) | ||||
−0.165162 | + | 0.986266i | \(0.552815\pi\) | |||||||
\(182\) | 1.82406e10 | 1.23230 | ||||||||
\(183\) | 6.35608e8 | 0.0418947 | ||||||||
\(184\) | −1.94789e10 | −1.25281 | ||||||||
\(185\) | 2.34258e10 | 1.47036 | ||||||||
\(186\) | 2.13794e9 | 0.130975 | ||||||||
\(187\) | −1.13689e8 | −0.00679879 | ||||||||
\(188\) | 2.18124e8 | 0.0127348 | ||||||||
\(189\) | 5.62561e9 | 0.320694 | ||||||||
\(190\) | −8.24587e9 | −0.459034 | ||||||||
\(191\) | 6.63400e9 | 0.360683 | 0.180341 | − | 0.983604i | \(-0.442280\pi\) | ||||
0.180341 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(192\) | −1.05738e10 | −0.561531 | ||||||||
\(193\) | −1.51066e10 | −0.783715 | −0.391858 | − | 0.920026i | \(-0.628167\pi\) | ||||
−0.391858 | + | 0.920026i | \(0.628167\pi\) | |||||||
\(194\) | 3.27929e10 | 1.66216 | ||||||||
\(195\) | −1.15236e10 | −0.570730 | ||||||||
\(196\) | 9.56631e8 | 0.0463012 | ||||||||
\(197\) | −1.63227e10 | −0.772135 | −0.386068 | − | 0.922470i | \(-0.626167\pi\) | ||||
−0.386068 | + | 0.922470i | \(0.626167\pi\) | |||||||
\(198\) | 1.70082e9 | 0.0786441 | ||||||||
\(199\) | −2.28537e9 | −0.103304 | −0.0516522 | − | 0.998665i | \(-0.516449\pi\) | ||||
−0.0516522 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(200\) | 1.86050e10 | 0.822231 | ||||||||
\(201\) | 8.33203e8 | 0.0360055 | ||||||||
\(202\) | −3.84458e10 | −1.62468 | ||||||||
\(203\) | 5.16857e10 | 2.13618 | ||||||||
\(204\) | −1.08632e7 | −0.000439157 0 | ||||||||
\(205\) | 5.01708e10 | 1.98408 | ||||||||
\(206\) | 6.50343e9 | 0.251617 | ||||||||
\(207\) | −1.11818e10 | −0.423296 | ||||||||
\(208\) | −2.02082e10 | −0.748588 | ||||||||
\(209\) | −2.15023e9 | −0.0779519 | ||||||||
\(210\) | −3.71894e10 | −1.31957 | ||||||||
\(211\) | 3.51058e10 | 1.21929 | 0.609647 | − | 0.792673i | \(-0.291311\pi\) | ||||
0.609647 | + | 0.792673i | \(0.291311\pi\) | |||||||
\(212\) | 1.19954e9 | 0.0407851 | ||||||||
\(213\) | −6.29793e9 | −0.209648 | ||||||||
\(214\) | −4.32421e10 | −1.40943 | ||||||||
\(215\) | −5.71660e9 | −0.182459 | ||||||||
\(216\) | −6.07406e9 | −0.189862 | ||||||||
\(217\) | −1.21900e10 | −0.373194 | ||||||||
\(218\) | −5.19643e10 | −1.55830 | ||||||||
\(219\) | −7.67817e9 | −0.225559 | ||||||||
\(220\) | −2.85553e8 | −0.00821836 | ||||||||
\(221\) | 7.55707e8 | 0.0213102 | ||||||||
\(222\) | 2.29828e10 | 0.635059 | ||||||||
\(223\) | 3.43402e10 | 0.929888 | 0.464944 | − | 0.885340i | \(-0.346074\pi\) | ||||
0.464944 | + | 0.885340i | \(0.346074\pi\) | |||||||
\(224\) | −3.27160e9 | −0.0868249 | ||||||||
\(225\) | 1.06801e10 | 0.277814 | ||||||||
\(226\) | −8.77549e9 | −0.223761 | ||||||||
\(227\) | −4.86859e10 | −1.21699 | −0.608495 | − | 0.793558i | \(-0.708226\pi\) | ||||
−0.608495 | + | 0.793558i | \(0.708226\pi\) | |||||||
\(228\) | −2.05458e8 | −0.00503519 | ||||||||
\(229\) | 4.13835e10 | 0.994416 | 0.497208 | − | 0.867631i | \(-0.334359\pi\) | ||||
0.497208 | + | 0.867631i | \(0.334359\pi\) | |||||||
\(230\) | 7.39197e10 | 1.74175 | ||||||||
\(231\) | −9.69768e9 | −0.224086 | ||||||||
\(232\) | −5.58058e10 | −1.26469 | ||||||||
\(233\) | 1.43437e10 | 0.318831 | 0.159415 | − | 0.987212i | \(-0.449039\pi\) | ||||
0.159415 | + | 0.987212i | \(0.449039\pi\) | |||||||
\(234\) | −1.13056e10 | −0.246503 | ||||||||
\(235\) | 3.09372e10 | 0.661722 | ||||||||
\(236\) | −1.61670e8 | −0.00339254 | ||||||||
\(237\) | −1.64152e10 | −0.337971 | ||||||||
\(238\) | 2.43885e9 | 0.0492708 | ||||||||
\(239\) | 6.98150e10 | 1.38407 | 0.692035 | − | 0.721864i | \(-0.256714\pi\) | ||||
0.692035 | + | 0.721864i | \(0.256714\pi\) | |||||||
\(240\) | 4.12010e10 | 0.801600 | ||||||||
\(241\) | 3.97202e10 | 0.758463 | 0.379232 | − | 0.925302i | \(-0.376188\pi\) | ||||
0.379232 | + | 0.925302i | \(0.376188\pi\) | |||||||
\(242\) | 5.11130e10 | 0.957993 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −1.04695e8 | −0.00189091 | ||||||||
\(245\) | 1.35682e11 | 2.40589 | ||||||||
\(246\) | 4.92219e10 | 0.856940 | ||||||||
\(247\) | 1.42929e10 | 0.244334 | ||||||||
\(248\) | 1.31617e10 | 0.220943 | ||||||||
\(249\) | 4.71289e10 | 0.776944 | ||||||||
\(250\) | 1.41097e10 | 0.228448 | ||||||||
\(251\) | 1.98403e10 | 0.315512 | 0.157756 | − | 0.987478i | \(-0.449574\pi\) | ||||
0.157756 | + | 0.987478i | \(0.449574\pi\) | |||||||
\(252\) | −9.26627e8 | −0.0144745 | ||||||||
\(253\) | 1.92756e10 | 0.295778 | ||||||||
\(254\) | 4.39495e9 | 0.0662525 | ||||||||
\(255\) | −1.54076e9 | −0.0228193 | ||||||||
\(256\) | 5.36858e9 | 0.0781231 | ||||||||
\(257\) | −8.77270e10 | −1.25440 | −0.627198 | − | 0.778860i | \(-0.715798\pi\) | ||||
−0.627198 | + | 0.778860i | \(0.715798\pi\) | |||||||
\(258\) | −5.60848e9 | −0.0788055 | ||||||||
\(259\) | −1.31042e11 | −1.80951 | ||||||||
\(260\) | 1.89811e9 | 0.0257598 | ||||||||
\(261\) | −3.20351e10 | −0.427310 | ||||||||
\(262\) | 2.85107e9 | 0.0373811 | ||||||||
\(263\) | −6.54118e10 | −0.843054 | −0.421527 | − | 0.906816i | \(-0.638506\pi\) | ||||
−0.421527 | + | 0.906816i | \(0.638506\pi\) | |||||||
\(264\) | 1.04707e10 | 0.132666 | ||||||||
\(265\) | 1.70134e11 | 2.11926 | ||||||||
\(266\) | 4.61267e10 | 0.564917 | ||||||||
\(267\) | 9.44078e10 | 1.13686 | ||||||||
\(268\) | −1.37242e8 | −0.00162510 | ||||||||
\(269\) | −3.14568e10 | −0.366293 | −0.183147 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183147 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(270\) | 2.30502e10 | 0.263960 | ||||||||
\(271\) | −2.31709e10 | −0.260964 | −0.130482 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130482 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(272\) | −2.70194e9 | −0.0299306 | ||||||||
\(273\) | 6.44618e10 | 0.702378 | ||||||||
\(274\) | 5.94695e10 | 0.637407 | ||||||||
\(275\) | −1.84108e10 | −0.194123 | ||||||||
\(276\) | 1.84181e9 | 0.0191054 | ||||||||
\(277\) | −1.40346e11 | −1.43233 | −0.716163 | − | 0.697933i | \(-0.754103\pi\) | ||||
−0.716163 | + | 0.697933i | \(0.754103\pi\) | |||||||
\(278\) | 3.98979e10 | 0.400635 | ||||||||
\(279\) | 7.55543e9 | 0.0746518 | ||||||||
\(280\) | −2.28948e11 | −2.22600 | ||||||||
\(281\) | −1.19944e11 | −1.14762 | −0.573812 | − | 0.818987i | \(-0.694536\pi\) | ||||
−0.573812 | + | 0.818987i | \(0.694536\pi\) | |||||||
\(282\) | 3.03521e10 | 0.285804 | ||||||||
\(283\) | −1.53845e11 | −1.42575 | −0.712875 | − | 0.701292i | \(-0.752607\pi\) | ||||
−0.712875 | + | 0.701292i | \(0.752607\pi\) | |||||||
\(284\) | 1.03737e9 | 0.00946239 | ||||||||
\(285\) | −2.91407e10 | −0.261637 | ||||||||
\(286\) | 1.94891e10 | 0.172244 | ||||||||
\(287\) | −2.80651e11 | −2.44173 | ||||||||
\(288\) | 2.02776e9 | 0.0173680 | ||||||||
\(289\) | −1.18487e11 | −0.999148 | ||||||||
\(290\) | 2.11775e11 | 1.75826 | ||||||||
\(291\) | 1.15889e11 | 0.947381 | ||||||||
\(292\) | 1.26472e9 | 0.0101805 | ||||||||
\(293\) | 1.90706e11 | 1.51168 | 0.755840 | − | 0.654756i | \(-0.227229\pi\) | ||||
0.755840 | + | 0.654756i | \(0.227229\pi\) | |||||||
\(294\) | 1.33116e11 | 1.03912 | ||||||||
\(295\) | −2.29301e10 | −0.176282 | ||||||||
\(296\) | 1.41488e11 | 1.07129 | ||||||||
\(297\) | 6.01068e9 | 0.0448249 | ||||||||
\(298\) | 1.75161e11 | 1.28666 | ||||||||
\(299\) | −1.28128e11 | −0.927093 | ||||||||
\(300\) | −1.75918e9 | −0.0125391 | ||||||||
\(301\) | 3.19782e10 | 0.224545 | ||||||||
\(302\) | 2.80273e11 | 1.93887 | ||||||||
\(303\) | −1.35867e11 | −0.926021 | ||||||||
\(304\) | −5.11024e10 | −0.343171 | ||||||||
\(305\) | −1.48492e10 | −0.0982547 | ||||||||
\(306\) | −1.51162e9 | −0.00985587 | ||||||||
\(307\) | −7.97764e10 | −0.512568 | −0.256284 | − | 0.966602i | \(-0.582498\pi\) | ||||
−0.256284 | + | 0.966602i | \(0.582498\pi\) | |||||||
\(308\) | 1.59736e9 | 0.0101140 | ||||||||
\(309\) | 2.29830e10 | 0.143415 | ||||||||
\(310\) | −4.99469e10 | −0.307172 | ||||||||
\(311\) | −2.22045e9 | −0.0134592 | −0.00672961 | − | 0.999977i | \(-0.502142\pi\) | ||||
−0.00672961 | + | 0.999977i | \(0.502142\pi\) | |||||||
\(312\) | −6.96004e10 | −0.415830 | ||||||||
\(313\) | 1.22486e11 | 0.721337 | 0.360668 | − | 0.932694i | \(-0.382549\pi\) | ||||
0.360668 | + | 0.932694i | \(0.382549\pi\) | |||||||
\(314\) | −1.34216e11 | −0.779148 | ||||||||
\(315\) | −1.31427e11 | −0.752117 | ||||||||
\(316\) | 2.70385e9 | 0.0152542 | ||||||||
\(317\) | 1.07146e11 | 0.595951 | 0.297975 | − | 0.954574i | \(-0.403689\pi\) | ||||
0.297975 | + | 0.954574i | \(0.403689\pi\) | |||||||
\(318\) | 1.66916e11 | 0.915328 | ||||||||
\(319\) | 5.52235e10 | 0.298584 | ||||||||
\(320\) | 2.47026e11 | 1.31695 | ||||||||
\(321\) | −1.52817e11 | −0.803337 | ||||||||
\(322\) | −4.13500e11 | −2.14350 | ||||||||
\(323\) | 1.91103e9 | 0.00976913 | ||||||||
\(324\) | 5.74329e8 | 0.00289540 | ||||||||
\(325\) | 1.22379e11 | 0.608461 | ||||||||
\(326\) | 3.28751e10 | 0.161209 | ||||||||
\(327\) | −1.83641e11 | −0.888187 | ||||||||
\(328\) | 3.03023e11 | 1.44559 | ||||||||
\(329\) | −1.73060e11 | −0.814358 | ||||||||
\(330\) | −3.97350e10 | −0.184442 | ||||||||
\(331\) | −2.06304e11 | −0.944676 | −0.472338 | − | 0.881418i | \(-0.656590\pi\) | ||||
−0.472338 | + | 0.881418i | \(0.656590\pi\) | |||||||
\(332\) | −7.76288e9 | −0.0350672 | ||||||||
\(333\) | 8.12207e10 | 0.361966 | ||||||||
\(334\) | 4.14953e11 | 1.82448 | ||||||||
\(335\) | −1.94654e10 | −0.0844428 | ||||||||
\(336\) | −2.30475e11 | −0.986500 | ||||||||
\(337\) | 1.93295e11 | 0.816368 | 0.408184 | − | 0.912900i | \(-0.366162\pi\) | ||||
0.408184 | + | 0.912900i | \(0.366162\pi\) | |||||||
\(338\) | 1.13512e11 | 0.473060 | ||||||||
\(339\) | −3.10124e10 | −0.127537 | ||||||||
\(340\) | 2.53787e8 | 0.00102995 | ||||||||
\(341\) | −1.30244e10 | −0.0521630 | ||||||||
\(342\) | −2.85896e10 | −0.113003 | ||||||||
\(343\) | −3.31828e11 | −1.29446 | ||||||||
\(344\) | −3.45273e10 | −0.132938 | ||||||||
\(345\) | 2.61230e11 | 0.992746 | ||||||||
\(346\) | 4.33636e10 | 0.162661 | ||||||||
\(347\) | −4.00675e11 | −1.48358 | −0.741788 | − | 0.670634i | \(-0.766022\pi\) | ||||
−0.741788 | + | 0.670634i | \(0.766022\pi\) | |||||||
\(348\) | 5.27669e9 | 0.0192866 | ||||||||
\(349\) | −2.78406e11 | −1.00453 | −0.502266 | − | 0.864713i | \(-0.667500\pi\) | ||||
−0.502266 | + | 0.864713i | \(0.667500\pi\) | |||||||
\(350\) | 3.94948e11 | 1.40681 | ||||||||
\(351\) | −3.99538e10 | −0.140500 | ||||||||
\(352\) | −3.49554e9 | −0.0121359 | ||||||||
\(353\) | −2.58537e10 | −0.0886209 | −0.0443105 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443105 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(354\) | −2.24965e10 | −0.0761376 | ||||||||
\(355\) | 1.47133e11 | 0.491681 | ||||||||
\(356\) | −1.55505e10 | −0.0513120 | ||||||||
\(357\) | 8.61886e9 | 0.0280830 | ||||||||
\(358\) | 1.53528e11 | 0.493984 | ||||||||
\(359\) | −2.86964e11 | −0.911807 | −0.455904 | − | 0.890029i | \(-0.650684\pi\) | ||||
−0.455904 | + | 0.890029i | \(0.650684\pi\) | |||||||
\(360\) | 1.41903e11 | 0.445278 | ||||||||
\(361\) | −2.86544e11 | −0.887991 | ||||||||
\(362\) | 1.09324e11 | 0.334601 | ||||||||
\(363\) | 1.80632e11 | 0.546029 | ||||||||
\(364\) | −1.06179e10 | −0.0317017 | ||||||||
\(365\) | 1.79379e11 | 0.528997 | ||||||||
\(366\) | −1.45684e10 | −0.0424371 | ||||||||
\(367\) | −2.90965e11 | −0.837227 | −0.418614 | − | 0.908164i | \(-0.637484\pi\) | ||||
−0.418614 | + | 0.908164i | \(0.637484\pi\) | |||||||
\(368\) | 4.58105e11 | 1.30212 | ||||||||
\(369\) | 1.73949e11 | 0.488432 | ||||||||
\(370\) | −5.36928e11 | −1.48939 | ||||||||
\(371\) | −9.51716e11 | −2.60810 | ||||||||
\(372\) | −1.24450e9 | −0.00336939 | ||||||||
\(373\) | 1.60534e11 | 0.429415 | 0.214708 | − | 0.976678i | \(-0.431120\pi\) | ||||
0.214708 | + | 0.976678i | \(0.431120\pi\) | |||||||
\(374\) | 2.60579e9 | 0.00688680 | ||||||||
\(375\) | 4.98634e10 | 0.130209 | ||||||||
\(376\) | 1.86856e11 | 0.482127 | ||||||||
\(377\) | −3.67078e11 | −0.935886 | ||||||||
\(378\) | −1.28941e11 | −0.324846 | ||||||||
\(379\) | −1.56835e10 | −0.0390451 | −0.0195226 | − | 0.999809i | \(-0.506215\pi\) | ||||
−0.0195226 | + | 0.999809i | \(0.506215\pi\) | |||||||
\(380\) | 4.79994e9 | 0.0118089 | ||||||||
\(381\) | 1.55317e10 | 0.0377620 | ||||||||
\(382\) | −1.52054e11 | −0.365352 | ||||||||
\(383\) | 3.05782e11 | 0.726134 | 0.363067 | − | 0.931763i | \(-0.381730\pi\) | ||||
0.363067 | + | 0.931763i | \(0.381730\pi\) | |||||||
\(384\) | 2.55172e11 | 0.598883 | ||||||||
\(385\) | 2.26559e11 | 0.525543 | ||||||||
\(386\) | 3.46248e11 | 0.793861 | ||||||||
\(387\) | −1.98202e10 | −0.0449169 | ||||||||
\(388\) | −1.90888e10 | −0.0427598 | ||||||||
\(389\) | −5.78332e11 | −1.28057 | −0.640286 | − | 0.768136i | \(-0.721184\pi\) | ||||
−0.640286 | + | 0.768136i | \(0.721184\pi\) | |||||||
\(390\) | 2.64124e11 | 0.578119 | ||||||||
\(391\) | −1.71313e10 | −0.0370677 | ||||||||
\(392\) | 8.19498e11 | 1.75291 | ||||||||
\(393\) | 1.00756e10 | 0.0213062 | ||||||||
\(394\) | 3.74121e11 | 0.782131 | ||||||||
\(395\) | 3.83495e11 | 0.792635 | ||||||||
\(396\) | −9.90054e8 | −0.00202316 | ||||||||
\(397\) | −7.31453e11 | −1.47785 | −0.738923 | − | 0.673790i | \(-0.764665\pi\) | ||||
−0.738923 | + | 0.673790i | \(0.764665\pi\) | |||||||
\(398\) | 5.23816e10 | 0.104642 | ||||||||
\(399\) | 1.63011e11 | 0.321987 | ||||||||
\(400\) | −4.37552e11 | −0.854593 | ||||||||
\(401\) | 9.78590e11 | 1.88995 | 0.944977 | − | 0.327137i | \(-0.106084\pi\) | ||||
0.944977 | + | 0.327137i | \(0.106084\pi\) | |||||||
\(402\) | −1.90973e10 | −0.0364716 | ||||||||
\(403\) | 8.65750e10 | 0.163501 | ||||||||
\(404\) | 2.23794e10 | 0.0417958 | ||||||||
\(405\) | 8.14589e10 | 0.150450 | ||||||||
\(406\) | −1.18465e12 | −2.16384 | ||||||||
\(407\) | −1.40012e11 | −0.252924 | ||||||||
\(408\) | −9.30592e9 | −0.0166260 | ||||||||
\(409\) | −3.33232e11 | −0.588833 | −0.294417 | − | 0.955677i | \(-0.595125\pi\) | ||||
−0.294417 | + | 0.955677i | \(0.595125\pi\) | |||||||
\(410\) | −1.14993e12 | −2.00976 | ||||||||
\(411\) | 2.10164e11 | 0.363304 | ||||||||
\(412\) | −3.78566e9 | −0.00647298 | ||||||||
\(413\) | 1.28269e11 | 0.216944 | ||||||||
\(414\) | 2.56290e11 | 0.428775 | ||||||||
\(415\) | −1.10103e12 | −1.82215 | ||||||||
\(416\) | 2.32353e10 | 0.0380390 | ||||||||
\(417\) | 1.40998e11 | 0.228350 | ||||||||
\(418\) | 4.92840e10 | 0.0789610 | ||||||||
\(419\) | 6.63685e11 | 1.05196 | 0.525980 | − | 0.850497i | \(-0.323699\pi\) | ||||
0.525980 | + | 0.850497i | \(0.323699\pi\) | |||||||
\(420\) | 2.16480e10 | 0.0339466 | ||||||||
\(421\) | 2.83675e11 | 0.440100 | 0.220050 | − | 0.975489i | \(-0.429378\pi\) | ||||
0.220050 | + | 0.975489i | \(0.429378\pi\) | |||||||
\(422\) | −8.04638e11 | −1.23508 | ||||||||
\(423\) | 1.07264e11 | 0.162900 | ||||||||
\(424\) | 1.02758e12 | 1.54408 | ||||||||
\(425\) | 1.63627e10 | 0.0243279 | ||||||||
\(426\) | 1.44351e11 | 0.212362 | ||||||||
\(427\) | 8.30651e10 | 0.120919 | ||||||||
\(428\) | 2.51713e10 | 0.0362584 | ||||||||
\(429\) | 6.88742e10 | 0.0981745 | ||||||||
\(430\) | 1.31026e11 | 0.184821 | ||||||||
\(431\) | 4.68713e11 | 0.654273 | 0.327137 | − | 0.944977i | \(-0.393916\pi\) | ||||
0.327137 | + | 0.944977i | \(0.393916\pi\) | |||||||
\(432\) | 1.42850e11 | 0.197334 | ||||||||
\(433\) | −5.38090e10 | −0.0735630 | −0.0367815 | − | 0.999323i | \(-0.511711\pi\) | ||||
−0.0367815 | + | 0.999323i | \(0.511711\pi\) | |||||||
\(434\) | 2.79399e11 | 0.378025 | ||||||||
\(435\) | 7.48409e11 | 1.00216 | ||||||||
\(436\) | 3.02486e10 | 0.0400881 | ||||||||
\(437\) | −3.24009e11 | −0.425002 | ||||||||
\(438\) | 1.75986e11 | 0.228478 | ||||||||
\(439\) | 9.15078e11 | 1.17589 | 0.587947 | − | 0.808900i | \(-0.299936\pi\) | ||||
0.587947 | + | 0.808900i | \(0.299936\pi\) | |||||||
\(440\) | −2.44619e11 | −0.311138 | ||||||||
\(441\) | 4.70429e11 | 0.592271 | ||||||||
\(442\) | −1.73211e10 | −0.0215861 | ||||||||
\(443\) | −9.22618e11 | −1.13816 | −0.569082 | − | 0.822281i | \(-0.692701\pi\) | ||||
−0.569082 | + | 0.822281i | \(0.692701\pi\) | |||||||
\(444\) | −1.33783e10 | −0.0163372 | ||||||||
\(445\) | −2.20557e12 | −2.66625 | ||||||||
\(446\) | −7.87089e11 | −0.941926 | ||||||||
\(447\) | 6.19014e11 | 0.733359 | ||||||||
\(448\) | −1.38184e12 | −1.62072 | ||||||||
\(449\) | 1.57214e12 | 1.82551 | 0.912754 | − | 0.408510i | \(-0.133952\pi\) | ||||
0.912754 | + | 0.408510i | \(0.133952\pi\) | |||||||
\(450\) | −2.44791e11 | −0.281410 | ||||||||
\(451\) | −2.99861e11 | −0.341292 | ||||||||
\(452\) | 5.10824e9 | 0.00575636 | ||||||||
\(453\) | 9.90478e11 | 1.10510 | ||||||||
\(454\) | 1.11590e12 | 1.23274 | ||||||||
\(455\) | −1.50597e12 | −1.64727 | ||||||||
\(456\) | −1.76005e11 | −0.190627 | ||||||||
\(457\) | 5.15006e11 | 0.552318 | 0.276159 | − | 0.961112i | \(-0.410938\pi\) | ||||
0.276159 | + | 0.961112i | \(0.410938\pi\) | |||||||
\(458\) | −9.48525e11 | −1.00729 | ||||||||
\(459\) | −5.34202e9 | −0.00561757 | ||||||||
\(460\) | −4.30288e10 | −0.0448073 | ||||||||
\(461\) | −1.01160e12 | −1.04317 | −0.521585 | − | 0.853199i | \(-0.674659\pi\) | ||||
−0.521585 | + | 0.853199i | \(0.674659\pi\) | |||||||
\(462\) | 2.22274e11 | 0.226986 | ||||||||
\(463\) | −7.03444e11 | −0.711402 | −0.355701 | − | 0.934600i | \(-0.615758\pi\) | ||||
−0.355701 | + | 0.934600i | \(0.615758\pi\) | |||||||
\(464\) | 1.31244e12 | 1.31447 | ||||||||
\(465\) | −1.76511e11 | −0.175079 | ||||||||
\(466\) | −3.28763e11 | −0.322958 | ||||||||
\(467\) | −1.33152e12 | −1.29545 | −0.647725 | − | 0.761874i | \(-0.724279\pi\) | ||||
−0.647725 | + | 0.761874i | \(0.724279\pi\) | |||||||
\(468\) | 6.58103e9 | 0.00634143 | ||||||||
\(469\) | 1.08888e11 | 0.103921 | ||||||||
\(470\) | −7.09091e11 | −0.670288 | ||||||||
\(471\) | −4.74315e11 | −0.444092 | ||||||||
\(472\) | −1.38494e11 | −0.128438 | ||||||||
\(473\) | 3.41670e10 | 0.0313857 | ||||||||
\(474\) | 3.76242e11 | 0.342346 | ||||||||
\(475\) | 3.09472e11 | 0.278933 | ||||||||
\(476\) | −1.41966e9 | −0.00126752 | ||||||||
\(477\) | 5.89879e11 | 0.521711 | ||||||||
\(478\) | −1.60018e12 | −1.40199 | ||||||||
\(479\) | 1.70657e12 | 1.48120 | 0.740599 | − | 0.671947i | \(-0.234542\pi\) | ||||
0.740599 | + | 0.671947i | \(0.234542\pi\) | |||||||
\(480\) | −4.73728e10 | −0.0407328 | ||||||||
\(481\) | 9.30678e11 | 0.792769 | ||||||||
\(482\) | −9.10400e11 | −0.768282 | ||||||||
\(483\) | −1.46130e12 | −1.22174 | ||||||||
\(484\) | −2.97530e10 | −0.0246449 | ||||||||
\(485\) | −2.70743e12 | −2.22187 | ||||||||
\(486\) | 7.99183e10 | 0.0649805 | ||||||||
\(487\) | −1.61398e12 | −1.30022 | −0.650112 | − | 0.759838i | \(-0.725278\pi\) | ||||
−0.650112 | + | 0.759838i | \(0.725278\pi\) | |||||||
\(488\) | −8.96867e10 | −0.0715878 | ||||||||
\(489\) | 1.16180e11 | 0.0918843 | ||||||||
\(490\) | −3.10988e12 | −2.43703 | ||||||||
\(491\) | −2.15992e12 | −1.67714 | −0.838572 | − | 0.544790i | \(-0.816609\pi\) | ||||
−0.838572 | + | 0.544790i | \(0.816609\pi\) | |||||||
\(492\) | −2.86522e10 | −0.0220452 | ||||||||
\(493\) | −4.90802e10 | −0.0374192 | ||||||||
\(494\) | −3.27598e11 | −0.247497 | ||||||||
\(495\) | −1.40423e11 | −0.105127 | ||||||||
\(496\) | −3.09538e11 | −0.229639 | ||||||||
\(497\) | −8.23052e11 | −0.605095 | ||||||||
\(498\) | −1.08021e12 | −0.787002 | ||||||||
\(499\) | −2.03228e12 | −1.46734 | −0.733670 | − | 0.679506i | \(-0.762194\pi\) | ||||
−0.733670 | + | 0.679506i | \(0.762194\pi\) | |||||||
\(500\) | −8.21330e9 | −0.00587696 | ||||||||
\(501\) | 1.46644e12 | 1.03990 | ||||||||
\(502\) | −4.54745e11 | −0.319596 | ||||||||
\(503\) | 6.31371e11 | 0.439773 | 0.219886 | − | 0.975525i | \(-0.429431\pi\) | ||||
0.219886 | + | 0.975525i | \(0.429431\pi\) | |||||||
\(504\) | −7.93795e11 | −0.547988 | ||||||||
\(505\) | 3.17414e12 | 2.17178 | ||||||||
\(506\) | −4.41804e11 | −0.299607 | ||||||||
\(507\) | 4.01148e11 | 0.269631 | ||||||||
\(508\) | −2.55831e9 | −0.00170438 | ||||||||
\(509\) | −2.03580e12 | −1.34433 | −0.672165 | − | 0.740401i | \(-0.734635\pi\) | ||||
−0.672165 | + | 0.740401i | \(0.734635\pi\) | |||||||
\(510\) | 3.53147e10 | 0.0231147 | ||||||||
\(511\) | −1.00343e12 | −0.651018 | ||||||||
\(512\) | 1.48989e12 | 0.958161 | ||||||||
\(513\) | −1.01035e11 | −0.0644086 | ||||||||
\(514\) | 2.01073e12 | 1.27063 | ||||||||
\(515\) | −5.36933e11 | −0.336347 | ||||||||
\(516\) | 3.26471e9 | 0.00202731 | ||||||||
\(517\) | −1.84906e11 | −0.113826 | ||||||||
\(518\) | 3.00353e12 | 1.83294 | ||||||||
\(519\) | 1.53246e11 | 0.0927120 | ||||||||
\(520\) | 1.62602e12 | 0.975237 | ||||||||
\(521\) | 1.62258e12 | 0.964796 | 0.482398 | − | 0.875952i | \(-0.339766\pi\) | ||||
0.482398 | + | 0.875952i | \(0.339766\pi\) | |||||||
\(522\) | 7.34255e11 | 0.432842 | ||||||||
\(523\) | 1.30110e12 | 0.760421 | 0.380210 | − | 0.924900i | \(-0.375852\pi\) | ||||
0.380210 | + | 0.924900i | \(0.375852\pi\) | |||||||
\(524\) | −1.65962e9 | −0.000961649 0 | ||||||||
\(525\) | 1.39574e12 | 0.801840 | ||||||||
\(526\) | 1.49926e12 | 0.853968 | ||||||||
\(527\) | 1.15755e10 | 0.00653720 | ||||||||
\(528\) | −2.46251e11 | −0.137888 | ||||||||
\(529\) | 1.10341e12 | 0.612613 | ||||||||
\(530\) | −3.89953e12 | −2.14670 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −2.68505e10 | −0.0145328 | ||||||||
\(533\) | 1.99322e12 | 1.06975 | ||||||||
\(534\) | −2.16386e12 | −1.15158 | ||||||||
\(535\) | 3.57013e12 | 1.88405 | ||||||||
\(536\) | −1.17568e11 | −0.0615245 | ||||||||
\(537\) | 5.42564e11 | 0.281557 | ||||||||
\(538\) | 7.21000e11 | 0.371035 | ||||||||
\(539\) | −8.10947e11 | −0.413850 | ||||||||
\(540\) | −1.34176e10 | −0.00679051 | ||||||||
\(541\) | −2.29207e12 | −1.15038 | −0.575189 | − | 0.818020i | \(-0.695072\pi\) | ||||
−0.575189 | + | 0.818020i | \(0.695072\pi\) | |||||||
\(542\) | 5.31084e11 | 0.264342 | ||||||||
\(543\) | 3.86349e11 | 0.190713 | ||||||||
\(544\) | 3.10668e9 | 0.00152090 | ||||||||
\(545\) | 4.29025e12 | 2.08304 | ||||||||
\(546\) | −1.47749e12 | −0.711470 | ||||||||
\(547\) | −3.98480e12 | −1.90311 | −0.951553 | − | 0.307484i | \(-0.900513\pi\) | ||||
−0.951553 | + | 0.307484i | \(0.900513\pi\) | |||||||
\(548\) | −3.46174e10 | −0.0163976 | ||||||||
\(549\) | −5.14842e10 | −0.0241879 | ||||||||
\(550\) | 4.21982e11 | 0.196636 | ||||||||
\(551\) | −9.28266e11 | −0.429033 | ||||||||
\(552\) | 1.57779e12 | 0.723308 | ||||||||
\(553\) | −2.14524e12 | −0.975468 | ||||||||
\(554\) | 3.21678e12 | 1.45087 | ||||||||
\(555\) | −1.89749e12 | −0.848910 | ||||||||
\(556\) | −2.32247e10 | −0.0103065 | ||||||||
\(557\) | 2.70211e12 | 1.18947 | 0.594736 | − | 0.803921i | \(-0.297257\pi\) | ||||
0.594736 | + | 0.803921i | \(0.297257\pi\) | |||||||
\(558\) | −1.73173e11 | −0.0756182 | ||||||||
\(559\) | −2.27113e11 | −0.0983760 | ||||||||
\(560\) | 5.38440e12 | 2.31362 | ||||||||
\(561\) | 9.20881e9 | 0.00392528 | ||||||||
\(562\) | 2.74915e12 | 1.16248 | ||||||||
\(563\) | 2.46879e12 | 1.03561 | 0.517805 | − | 0.855498i | \(-0.326749\pi\) | ||||
0.517805 | + | 0.855498i | \(0.326749\pi\) | |||||||
\(564\) | −1.76680e10 | −0.00735245 | ||||||||
\(565\) | 7.24517e11 | 0.299110 | ||||||||
\(566\) | 3.52617e12 | 1.44421 | ||||||||
\(567\) | −4.55674e11 | −0.185153 | ||||||||
\(568\) | 8.88662e11 | 0.358236 | ||||||||
\(569\) | 2.28396e12 | 0.913446 | 0.456723 | − | 0.889609i | \(-0.349023\pi\) | ||||
0.456723 | + | 0.889609i | \(0.349023\pi\) | |||||||
\(570\) | 6.67915e11 | 0.265024 | ||||||||
\(571\) | 4.03714e11 | 0.158932 | 0.0794660 | − | 0.996838i | \(-0.474678\pi\) | ||||
0.0794660 | + | 0.996838i | \(0.474678\pi\) | |||||||
\(572\) | −1.13447e10 | −0.00443108 | ||||||||
\(573\) | −5.37354e11 | −0.208240 | ||||||||
\(574\) | 6.43262e12 | 2.47334 | ||||||||
\(575\) | −2.77425e12 | −1.05838 | ||||||||
\(576\) | 8.56475e11 | 0.324200 | ||||||||
\(577\) | 7.02747e10 | 0.0263942 | 0.0131971 | − | 0.999913i | \(-0.495799\pi\) | ||||
0.0131971 | + | 0.999913i | \(0.495799\pi\) | |||||||
\(578\) | 2.71576e12 | 1.01208 | ||||||||
\(579\) | 1.22363e12 | 0.452478 | ||||||||
\(580\) | −1.23275e11 | −0.0452323 | ||||||||
\(581\) | 6.15909e12 | 2.24246 | ||||||||
\(582\) | −2.65622e12 | −0.959646 | ||||||||
\(583\) | −1.01686e12 | −0.364546 | ||||||||
\(584\) | 1.08342e12 | 0.385424 | ||||||||
\(585\) | 9.33408e11 | 0.329511 | ||||||||
\(586\) | −4.37105e12 | −1.53125 | ||||||||
\(587\) | −7.87103e11 | −0.273628 | −0.136814 | − | 0.990597i | \(-0.543686\pi\) | ||||
−0.136814 | + | 0.990597i | \(0.543686\pi\) | |||||||
\(588\) | −7.74871e10 | −0.0267320 | ||||||||
\(589\) | 2.18930e11 | 0.0749527 | ||||||||
\(590\) | 5.25566e11 | 0.178564 | ||||||||
\(591\) | 1.32214e12 | 0.445793 | ||||||||
\(592\) | −3.32752e12 | −1.11346 | ||||||||
\(593\) | −2.04023e12 | −0.677536 | −0.338768 | − | 0.940870i | \(-0.610010\pi\) | ||||
−0.338768 | + | 0.940870i | \(0.610010\pi\) | |||||||
\(594\) | −1.37767e11 | −0.0454052 | ||||||||
\(595\) | −2.01355e11 | −0.0658623 | ||||||||
\(596\) | −1.01961e11 | −0.0331000 | ||||||||
\(597\) | 1.85115e11 | 0.0596428 | ||||||||
\(598\) | 2.93673e12 | 0.939094 | ||||||||
\(599\) | 5.37648e12 | 1.70638 | 0.853192 | − | 0.521596i | \(-0.174663\pi\) | ||||
0.853192 | + | 0.521596i | \(0.174663\pi\) | |||||||
\(600\) | −1.50700e12 | −0.474715 | ||||||||
\(601\) | −1.55803e12 | −0.487125 | −0.243562 | − | 0.969885i | \(-0.578316\pi\) | ||||
−0.243562 | + | 0.969885i | \(0.578316\pi\) | |||||||
\(602\) | −7.32950e11 | −0.227452 | ||||||||
\(603\) | −6.74894e10 | −0.0207878 | ||||||||
\(604\) | −1.63148e11 | −0.0498786 | ||||||||
\(605\) | −4.21996e12 | −1.28059 | ||||||||
\(606\) | 3.11411e12 | 0.938009 | ||||||||
\(607\) | −4.79310e12 | −1.43307 | −0.716535 | − | 0.697552i | \(-0.754273\pi\) | ||||
−0.716535 | + | 0.697552i | \(0.754273\pi\) | |||||||
\(608\) | 5.87574e10 | 0.0174380 | ||||||||
\(609\) | −4.18654e12 | −1.23332 | ||||||||
\(610\) | 3.40349e11 | 0.0995267 | ||||||||
\(611\) | 1.22910e12 | 0.356780 | ||||||||
\(612\) | 8.79916e8 | 0.000253548 0 | ||||||||
\(613\) | −5.79540e12 | −1.65772 | −0.828861 | − | 0.559455i | \(-0.811010\pi\) | ||||
−0.828861 | + | 0.559455i | \(0.811010\pi\) | |||||||
\(614\) | 1.82850e12 | 0.519203 | ||||||||
\(615\) | −4.06383e12 | −1.14551 | ||||||||
\(616\) | 1.36838e12 | 0.382907 | ||||||||
\(617\) | −2.65602e12 | −0.737815 | −0.368908 | − | 0.929466i | \(-0.620268\pi\) | ||||
−0.368908 | + | 0.929466i | \(0.620268\pi\) | |||||||
\(618\) | −5.26778e11 | −0.145271 | ||||||||
\(619\) | −2.06524e12 | −0.565410 | −0.282705 | − | 0.959207i | \(-0.591232\pi\) | ||||
−0.282705 | + | 0.959207i | \(0.591232\pi\) | |||||||
\(620\) | 2.90742e10 | 0.00790216 | ||||||||
\(621\) | 9.05723e11 | 0.244390 | ||||||||
\(622\) | 5.08936e10 | 0.0136335 | ||||||||
\(623\) | 1.23378e13 | 3.28127 | ||||||||
\(624\) | 1.63686e12 | 0.432197 | ||||||||
\(625\) | −4.34424e12 | −1.13882 | ||||||||
\(626\) | −2.80743e12 | −0.730675 | ||||||||
\(627\) | 1.74169e11 | 0.0450055 | ||||||||
\(628\) | 7.81273e10 | 0.0200440 | ||||||||
\(629\) | 1.24436e11 | 0.0316971 | ||||||||
\(630\) | 3.01234e12 | 0.761854 | ||||||||
\(631\) | 1.41149e12 | 0.354443 | 0.177222 | − | 0.984171i | \(-0.443289\pi\) | ||||
0.177222 | + | 0.984171i | \(0.443289\pi\) | |||||||
\(632\) | 2.31625e12 | 0.577509 | ||||||||
\(633\) | −2.84357e12 | −0.703959 | ||||||||
\(634\) | −2.45583e12 | −0.603666 | ||||||||
\(635\) | −3.62853e11 | −0.0885624 | ||||||||
\(636\) | −9.71624e10 | −0.0235473 | ||||||||
\(637\) | 5.39048e12 | 1.29718 | ||||||||
\(638\) | −1.26574e12 | −0.302449 | ||||||||
\(639\) | 5.10132e11 | 0.121040 | ||||||||
\(640\) | −5.96137e12 | −1.40455 | ||||||||
\(641\) | 2.33049e12 | 0.545238 | 0.272619 | − | 0.962122i | \(-0.412110\pi\) | ||||
0.272619 | + | 0.962122i | \(0.412110\pi\) | |||||||
\(642\) | 3.50261e12 | 0.813737 | ||||||||
\(643\) | 4.60509e12 | 1.06240 | 0.531201 | − | 0.847246i | \(-0.321741\pi\) | ||||
0.531201 | + | 0.847246i | \(0.321741\pi\) | |||||||
\(644\) | 2.40700e11 | 0.0551428 | ||||||||
\(645\) | 4.63044e11 | 0.105343 | ||||||||
\(646\) | −4.38014e10 | −0.00989560 | ||||||||
\(647\) | 1.96037e11 | 0.0439815 | 0.0219907 | − | 0.999758i | \(-0.493000\pi\) | ||||
0.0219907 | + | 0.999758i | \(0.493000\pi\) | |||||||
\(648\) | 4.91999e11 | 0.109617 | ||||||||
\(649\) | 1.37049e11 | 0.0303232 | ||||||||
\(650\) | −2.80497e12 | −0.616338 | ||||||||
\(651\) | 9.87390e11 | 0.215464 | ||||||||
\(652\) | −1.91367e10 | −0.00414718 | ||||||||
\(653\) | −2.50898e12 | −0.539993 | −0.269997 | − | 0.962861i | \(-0.587023\pi\) | ||||
−0.269997 | + | 0.962861i | \(0.587023\pi\) | |||||||
\(654\) | 4.20911e12 | 0.899685 | ||||||||
\(655\) | −2.35389e11 | −0.0499689 | ||||||||
\(656\) | −7.12651e12 | −1.50248 | ||||||||
\(657\) | 6.21932e11 | 0.130226 | ||||||||
\(658\) | 3.96660e12 | 0.824900 | ||||||||
\(659\) | 3.10145e12 | 0.640591 | 0.320296 | − | 0.947318i | \(-0.396218\pi\) | ||||
0.320296 | + | 0.947318i | \(0.396218\pi\) | |||||||
\(660\) | 2.31298e10 | 0.00474487 | ||||||||
\(661\) | 2.50610e12 | 0.510612 | 0.255306 | − | 0.966860i | \(-0.417824\pi\) | ||||
0.255306 | + | 0.966860i | \(0.417824\pi\) | |||||||
\(662\) | 4.72857e12 | 0.956905 | ||||||||
\(663\) | −6.12123e10 | −0.0123035 | ||||||||
\(664\) | −6.65006e12 | −1.32761 | ||||||||
\(665\) | −3.80829e12 | −0.755148 | ||||||||
\(666\) | −1.86161e12 | −0.366652 | ||||||||
\(667\) | 8.32140e12 | 1.62791 | ||||||||
\(668\) | −2.41545e11 | −0.0469359 | ||||||||
\(669\) | −2.78156e12 | −0.536871 | ||||||||
\(670\) | 4.46154e11 | 0.0855359 | ||||||||
\(671\) | 8.87509e10 | 0.0169013 | ||||||||
\(672\) | 2.65000e11 | 0.0501284 | ||||||||
\(673\) | −3.21035e12 | −0.603232 | −0.301616 | − | 0.953430i | \(-0.597526\pi\) | ||||
−0.301616 | + | 0.953430i | \(0.597526\pi\) | |||||||
\(674\) | −4.43039e12 | −0.826936 | ||||||||
\(675\) | −8.65087e11 | −0.160396 | ||||||||
\(676\) | −6.60755e10 | −0.0121697 | ||||||||
\(677\) | −4.53361e12 | −0.829460 | −0.414730 | − | 0.909945i | \(-0.636124\pi\) | ||||
−0.414730 | + | 0.909945i | \(0.636124\pi\) | |||||||
\(678\) | 7.10815e11 | 0.129188 | ||||||||
\(679\) | 1.51451e13 | 2.73438 | ||||||||
\(680\) | 2.17407e11 | 0.0389926 | ||||||||
\(681\) | 3.94356e12 | 0.702629 | ||||||||
\(682\) | 2.98523e11 | 0.0528383 | ||||||||
\(683\) | 2.98484e12 | 0.524841 | 0.262421 | − | 0.964954i | \(-0.415479\pi\) | ||||
0.262421 | + | 0.964954i | \(0.415479\pi\) | |||||||
\(684\) | 1.66421e10 | 0.00290707 | ||||||||
\(685\) | −4.90989e12 | −0.852048 | ||||||||
\(686\) | 7.60561e12 | 1.31122 | ||||||||
\(687\) | −3.35207e12 | −0.574126 | ||||||||
\(688\) | 8.12014e11 | 0.138171 | ||||||||
\(689\) | 6.75921e12 | 1.14264 | ||||||||
\(690\) | −5.98749e12 | −1.00560 | ||||||||
\(691\) | 3.29209e12 | 0.549314 | 0.274657 | − | 0.961542i | \(-0.411436\pi\) | ||||
0.274657 | + | 0.961542i | \(0.411436\pi\) | |||||||
\(692\) | −2.52421e10 | −0.00418454 | ||||||||
\(693\) | 7.85512e11 | 0.129376 | ||||||||
\(694\) | 9.18361e12 | 1.50278 | ||||||||
\(695\) | −3.29403e12 | −0.535545 | ||||||||
\(696\) | 4.52027e12 | 0.730168 | ||||||||
\(697\) | 2.66503e11 | 0.0427716 | ||||||||
\(698\) | 6.38116e12 | 1.01754 | ||||||||
\(699\) | −1.16184e12 | −0.184077 | ||||||||
\(700\) | −2.29900e11 | −0.0361908 | ||||||||
\(701\) | 3.95680e11 | 0.0618889 | 0.0309445 | − | 0.999521i | \(-0.490148\pi\) | ||||
0.0309445 | + | 0.999521i | \(0.490148\pi\) | |||||||
\(702\) | 9.15755e11 | 0.142319 | ||||||||
\(703\) | 2.35350e12 | 0.363425 | ||||||||
\(704\) | −1.47643e12 | −0.226535 | ||||||||
\(705\) | −2.50591e12 | −0.382045 | ||||||||
\(706\) | 5.92575e11 | 0.0897682 | ||||||||
\(707\) | −1.77559e13 | −2.67273 | ||||||||
\(708\) | 1.30952e10 | 0.00195868 | ||||||||
\(709\) | −2.61919e12 | −0.389278 | −0.194639 | − | 0.980875i | \(-0.562353\pi\) | ||||
−0.194639 | + | 0.980875i | \(0.562353\pi\) | |||||||
\(710\) | −3.37235e12 | −0.498047 | ||||||||
\(711\) | 1.32963e12 | 0.195127 | ||||||||
\(712\) | −1.33213e13 | −1.94262 | ||||||||
\(713\) | −1.96259e12 | −0.284398 | ||||||||
\(714\) | −1.97547e11 | −0.0284465 | ||||||||
\(715\) | −1.60905e12 | −0.230246 | ||||||||
\(716\) | −8.93689e10 | −0.0127080 | ||||||||
\(717\) | −5.65501e12 | −0.799093 | ||||||||
\(718\) | 6.57732e12 | 0.923611 | ||||||||
\(719\) | −1.29488e13 | −1.80697 | −0.903484 | − | 0.428621i | \(-0.859000\pi\) | ||||
−0.903484 | + | 0.428621i | \(0.859000\pi\) | |||||||
\(720\) | −3.33728e12 | −0.462804 | ||||||||
\(721\) | 3.00356e12 | 0.413930 | ||||||||
\(722\) | 6.56768e12 | 0.899487 | ||||||||
\(723\) | −3.21733e12 | −0.437899 | ||||||||
\(724\) | −6.36379e10 | −0.00860780 | ||||||||
\(725\) | −7.94805e12 | −1.06841 | ||||||||
\(726\) | −4.14015e12 | −0.553097 | ||||||||
\(727\) | −9.17093e12 | −1.21761 | −0.608806 | − | 0.793319i | \(-0.708351\pi\) | ||||
−0.608806 | + | 0.793319i | \(0.708351\pi\) | |||||||
\(728\) | −9.09581e12 | −1.20019 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −4.11142e12 | −0.535845 | ||||||||
\(731\) | −3.03661e10 | −0.00393334 | ||||||||
\(732\) | 8.48027e9 | 0.00109172 | ||||||||
\(733\) | −9.05826e12 | −1.15898 | −0.579492 | − | 0.814978i | \(-0.696749\pi\) | ||||
−0.579492 | + | 0.814978i | \(0.696749\pi\) | |||||||
\(734\) | 6.66902e12 | 0.848066 | ||||||||
\(735\) | −1.09902e13 | −1.38904 | ||||||||
\(736\) | −5.26728e11 | −0.0661662 | ||||||||
\(737\) | 1.16341e11 | 0.0145255 | ||||||||
\(738\) | −3.98697e12 | −0.494755 | ||||||||
\(739\) | 1.23920e13 | 1.52842 | 0.764208 | − | 0.644970i | \(-0.223130\pi\) | ||||
0.764208 | + | 0.644970i | \(0.223130\pi\) | |||||||
\(740\) | 3.12547e11 | 0.0383154 | ||||||||
\(741\) | −1.15772e12 | −0.141066 | ||||||||
\(742\) | 2.18136e13 | 2.64187 | ||||||||
\(743\) | −5.77385e12 | −0.695050 | −0.347525 | − | 0.937671i | \(-0.612978\pi\) | ||||
−0.347525 | + | 0.937671i | \(0.612978\pi\) | |||||||
\(744\) | −1.06610e12 | −0.127562 | ||||||||
\(745\) | −1.44615e13 | −1.71993 | ||||||||
\(746\) | −3.67949e12 | −0.434974 | ||||||||
\(747\) | −3.81744e12 | −0.448569 | ||||||||
\(748\) | −1.51684e9 | −0.000177167 0 | ||||||||
\(749\) | −1.99710e13 | −2.31863 | ||||||||
\(750\) | −1.14289e12 | −0.131895 | ||||||||
\(751\) | 1.09139e13 | 1.25198 | 0.625991 | − | 0.779830i | \(-0.284695\pi\) | ||||
0.625991 | + | 0.779830i | \(0.284695\pi\) | |||||||
\(752\) | −4.39448e12 | −0.501103 | ||||||||
\(753\) | −1.60706e12 | −0.182161 | ||||||||
\(754\) | 8.41356e12 | 0.948001 | ||||||||
\(755\) | −2.31397e13 | −2.59177 | ||||||||
\(756\) | 7.50568e10 | 0.00835684 | ||||||||
\(757\) | 4.84513e12 | 0.536259 | 0.268129 | − | 0.963383i | \(-0.413595\pi\) | ||||
0.268129 | + | 0.963383i | \(0.413595\pi\) | |||||||
\(758\) | 3.59472e11 | 0.0395506 | ||||||||
\(759\) | −1.56133e12 | −0.170768 | ||||||||
\(760\) | 4.11187e12 | 0.447072 | ||||||||
\(761\) | 4.06480e12 | 0.439348 | 0.219674 | − | 0.975573i | \(-0.429501\pi\) | ||||
0.219674 | + | 0.975573i | \(0.429501\pi\) | |||||||
\(762\) | −3.55991e11 | −0.0382509 | ||||||||
\(763\) | −2.39993e13 | −2.56353 | ||||||||
\(764\) | 8.85108e10 | 0.00939888 | ||||||||
\(765\) | 1.24801e11 | 0.0131748 | ||||||||
\(766\) | −7.00862e12 | −0.735534 | ||||||||
\(767\) | −9.10985e11 | −0.0950456 | ||||||||
\(768\) | −4.34855e11 | −0.0451044 | ||||||||
\(769\) | −3.72731e12 | −0.384351 | −0.192175 | − | 0.981361i | \(-0.561554\pi\) | ||||
−0.192175 | + | 0.981361i | \(0.561554\pi\) | |||||||
\(770\) | −5.19281e12 | −0.532346 | ||||||||
\(771\) | 7.10589e12 | 0.724225 | ||||||||
\(772\) | −2.01552e11 | −0.0204225 | ||||||||
\(773\) | 9.34605e12 | 0.941500 | 0.470750 | − | 0.882267i | \(-0.343983\pi\) | ||||
0.470750 | + | 0.882267i | \(0.343983\pi\) | |||||||
\(774\) | 4.54287e11 | 0.0454984 | ||||||||
\(775\) | 1.87454e12 | 0.186654 | ||||||||
\(776\) | −1.63524e13 | −1.61884 | ||||||||
\(777\) | 1.06144e13 | 1.04472 | ||||||||
\(778\) | 1.32556e13 | 1.29715 | ||||||||
\(779\) | 5.04045e12 | 0.490400 | ||||||||
\(780\) | −1.53747e11 | −0.0148724 | ||||||||
\(781\) | −8.79389e11 | −0.0845769 | ||||||||
\(782\) | 3.92656e11 | 0.0375475 | ||||||||
\(783\) | 2.59484e12 | 0.246708 | ||||||||
\(784\) | −1.92730e13 | −1.82191 | ||||||||
\(785\) | 1.10810e13 | 1.04152 | ||||||||
\(786\) | −2.30937e11 | −0.0215820 | ||||||||
\(787\) | 2.89984e12 | 0.269456 | 0.134728 | − | 0.990883i | \(-0.456984\pi\) | ||||
0.134728 | + | 0.990883i | \(0.456984\pi\) | |||||||
\(788\) | −2.17777e11 | −0.0201207 | ||||||||
\(789\) | 5.29836e12 | 0.486738 | ||||||||
\(790\) | −8.78984e12 | −0.802896 | ||||||||
\(791\) | −4.05289e12 | −0.368104 | ||||||||
\(792\) | −8.48129e11 | −0.0765947 | ||||||||
\(793\) | −5.89939e11 | −0.0529759 | ||||||||
\(794\) | 1.67651e13 | 1.49698 | ||||||||
\(795\) | −1.37809e13 | −1.22356 | ||||||||
\(796\) | −3.04914e10 | −0.00269196 | ||||||||
\(797\) | 1.61987e13 | 1.42206 | 0.711032 | − | 0.703160i | \(-0.248228\pi\) | ||||
0.711032 | + | 0.703160i | \(0.248228\pi\) | |||||||
\(798\) | −3.73626e12 | −0.326155 | ||||||||
\(799\) | 1.64336e11 | 0.0142650 | ||||||||
\(800\) | 5.03096e11 | 0.0434256 | ||||||||
\(801\) | −7.64704e12 | −0.656367 | ||||||||
\(802\) | −2.24296e13 | −1.91442 | ||||||||
\(803\) | −1.07211e12 | −0.0909957 | ||||||||
\(804\) | 1.11166e10 | 0.000938251 0 | ||||||||
\(805\) | 3.41392e13 | 2.86531 | ||||||||
\(806\) | −1.98433e12 | −0.165617 | ||||||||
\(807\) | 2.54800e12 | 0.211479 | ||||||||
\(808\) | 1.91713e13 | 1.58234 | ||||||||
\(809\) | −2.05504e13 | −1.68676 | −0.843379 | − | 0.537320i | \(-0.819437\pi\) | ||||
−0.843379 | + | 0.537320i | \(0.819437\pi\) | |||||||
\(810\) | −1.86707e12 | −0.152397 | ||||||||
\(811\) | 1.71119e13 | 1.38901 | 0.694505 | − | 0.719488i | \(-0.255624\pi\) | ||||
0.694505 | + | 0.719488i | \(0.255624\pi\) | |||||||
\(812\) | 6.89590e11 | 0.0556658 | ||||||||
\(813\) | 1.87684e12 | 0.150668 | ||||||||
\(814\) | 3.20912e12 | 0.256198 | ||||||||
\(815\) | −2.71422e12 | −0.215494 | ||||||||
\(816\) | 2.18857e11 | 0.0172804 | ||||||||
\(817\) | −5.74322e11 | −0.0450979 | ||||||||
\(818\) | 7.63780e12 | 0.596456 | ||||||||
\(819\) | −5.22141e12 | −0.405518 | ||||||||
\(820\) | 6.69378e11 | 0.0517022 | ||||||||
\(821\) | −1.29396e13 | −0.993978 | −0.496989 | − | 0.867757i | \(-0.665561\pi\) | ||||
−0.496989 | + | 0.867757i | \(0.665561\pi\) | |||||||
\(822\) | −4.81703e12 | −0.368007 | ||||||||
\(823\) | 1.15453e13 | 0.877212 | 0.438606 | − | 0.898680i | \(-0.355472\pi\) | ||||
0.438606 | + | 0.898680i | \(0.355472\pi\) | |||||||
\(824\) | −3.24299e12 | −0.245060 | ||||||||
\(825\) | 1.49128e12 | 0.112077 | ||||||||
\(826\) | −2.93997e12 | −0.219752 | ||||||||
\(827\) | 1.58069e13 | 1.17509 | 0.587546 | − | 0.809190i | \(-0.300094\pi\) | ||||
0.587546 | + | 0.809190i | \(0.300094\pi\) | |||||||
\(828\) | −1.49187e11 | −0.0110305 | ||||||||
\(829\) | 1.88409e12 | 0.138550 | 0.0692750 | − | 0.997598i | \(-0.477931\pi\) | ||||
0.0692750 | + | 0.997598i | \(0.477931\pi\) | |||||||
\(830\) | 2.52361e13 | 1.84574 | ||||||||
\(831\) | 1.13680e13 | 0.826954 | ||||||||
\(832\) | 9.81404e12 | 0.710056 | ||||||||
\(833\) | 7.20733e11 | 0.0518647 | ||||||||
\(834\) | −3.23173e12 | −0.231306 | ||||||||
\(835\) | −3.42592e13 | −2.43886 | ||||||||
\(836\) | −2.86884e10 | −0.00203132 | ||||||||
\(837\) | −6.11990e11 | −0.0431002 | ||||||||
\(838\) | −1.52119e13 | −1.06558 | ||||||||
\(839\) | −1.77244e13 | −1.23493 | −0.617465 | − | 0.786598i | \(-0.711840\pi\) | ||||
−0.617465 | + | 0.786598i | \(0.711840\pi\) | |||||||
\(840\) | 1.85448e13 | 1.28518 | ||||||||
\(841\) | 9.33315e12 | 0.643348 | ||||||||
\(842\) | −6.50193e12 | −0.445798 | ||||||||
\(843\) | 9.71545e12 | 0.662580 | ||||||||
\(844\) | 4.68382e11 | 0.0317730 | ||||||||
\(845\) | −9.37170e12 | −0.632358 | ||||||||
\(846\) | −2.45852e12 | −0.165009 | ||||||||
\(847\) | 2.36061e13 | 1.57598 | ||||||||
\(848\) | −2.41667e13 | −1.60486 | ||||||||
\(849\) | 1.24614e13 | 0.823157 | ||||||||
\(850\) | −3.75039e11 | −0.0246429 | ||||||||
\(851\) | −2.10978e13 | −1.37897 | ||||||||
\(852\) | −8.40269e10 | −0.00546312 | ||||||||
\(853\) | 4.32299e12 | 0.279585 | 0.139792 | − | 0.990181i | \(-0.455356\pi\) | ||||
0.139792 | + | 0.990181i | \(0.455356\pi\) | |||||||
\(854\) | −1.90388e12 | −0.122484 | ||||||||
\(855\) | 2.36040e12 | 0.151056 | ||||||||
\(856\) | 2.15630e13 | 1.37271 | ||||||||
\(857\) | −1.08195e13 | −0.685164 | −0.342582 | − | 0.939488i | \(-0.611301\pi\) | ||||
−0.342582 | + | 0.939488i | \(0.611301\pi\) | |||||||
\(858\) | −1.57862e12 | −0.0994454 | ||||||||
\(859\) | 1.50394e13 | 0.942453 | 0.471227 | − | 0.882012i | \(-0.343811\pi\) | ||||
0.471227 | + | 0.882012i | \(0.343811\pi\) | |||||||
\(860\) | −7.62708e10 | −0.00475461 | ||||||||
\(861\) | 2.27327e13 | 1.40974 | ||||||||
\(862\) | −1.07431e13 | −0.662743 | ||||||||
\(863\) | −6.00473e12 | −0.368507 | −0.184253 | − | 0.982879i | \(-0.558987\pi\) | ||||
−0.184253 | + | 0.982879i | \(0.558987\pi\) | |||||||
\(864\) | −1.64248e11 | −0.0100274 | ||||||||
\(865\) | −3.58016e12 | −0.217435 | ||||||||
\(866\) | 1.23332e12 | 0.0745154 | ||||||||
\(867\) | 9.59743e12 | 0.576858 | ||||||||
\(868\) | −1.62639e11 | −0.00972491 | ||||||||
\(869\) | −2.29208e12 | −0.136346 | ||||||||
\(870\) | −1.71538e13 | −1.01513 | ||||||||
\(871\) | −7.73337e11 | −0.0455289 | ||||||||
\(872\) | 2.59124e13 | 1.51769 | ||||||||
\(873\) | −9.38703e12 | −0.546971 | ||||||||
\(874\) | 7.42640e12 | 0.430504 | ||||||||
\(875\) | 6.51646e12 | 0.375816 | ||||||||
\(876\) | −1.02442e11 | −0.00587773 | ||||||||
\(877\) | −2.28028e13 | −1.30164 | −0.650820 | − | 0.759232i | \(-0.725575\pi\) | ||||
−0.650820 | + | 0.759232i | \(0.725575\pi\) | |||||||
\(878\) | −2.09739e13 | −1.19112 | ||||||||
\(879\) | −1.54472e13 | −0.872769 | ||||||||
\(880\) | 5.75296e12 | 0.323385 | ||||||||
\(881\) | 4.31310e12 | 0.241211 | 0.120606 | − | 0.992700i | \(-0.461516\pi\) | ||||
0.120606 | + | 0.992700i | \(0.461516\pi\) | |||||||
\(882\) | −1.07824e13 | −0.599938 | ||||||||
\(883\) | −1.25619e13 | −0.695397 | −0.347699 | − | 0.937606i | \(-0.613037\pi\) | ||||
−0.347699 | + | 0.937606i | \(0.613037\pi\) | |||||||
\(884\) | 1.00826e10 | 0.000555314 0 | ||||||||
\(885\) | 1.85734e12 | 0.101776 | ||||||||
\(886\) | 2.11467e13 | 1.15290 | ||||||||
\(887\) | 4.26918e12 | 0.231573 | 0.115787 | − | 0.993274i | \(-0.463061\pi\) | ||||
0.115787 | + | 0.993274i | \(0.463061\pi\) | |||||||
\(888\) | −1.14605e13 | −0.618511 | ||||||||
\(889\) | 2.02977e12 | 0.108991 | ||||||||
\(890\) | 5.05525e13 | 2.70077 | ||||||||
\(891\) | −4.86865e11 | −0.0258797 | ||||||||
\(892\) | 4.58166e11 | 0.0242316 | ||||||||
\(893\) | 3.10813e12 | 0.163556 | ||||||||
\(894\) | −1.41880e13 | −0.742853 | ||||||||
\(895\) | −1.26755e13 | −0.660329 | ||||||||
\(896\) | 3.33474e13 | 1.72853 | ||||||||
\(897\) | 1.03784e13 | 0.535257 | ||||||||
\(898\) | −3.60341e13 | −1.84914 | ||||||||
\(899\) | −5.62270e12 | −0.287096 | ||||||||
\(900\) | 1.42494e11 | 0.00723943 | ||||||||
\(901\) | 9.03739e11 | 0.0456858 | ||||||||
\(902\) | 6.87292e12 | 0.345710 | ||||||||
\(903\) | −2.59023e12 | −0.129641 | ||||||||
\(904\) | 4.37597e12 | 0.217930 | ||||||||
\(905\) | −9.02596e12 | −0.447275 | ||||||||
\(906\) | −2.27021e13 | −1.11941 | ||||||||
\(907\) | 2.50023e13 | 1.22672 | 0.613362 | − | 0.789802i | \(-0.289817\pi\) | ||||
0.613362 | + | 0.789802i | \(0.289817\pi\) | |||||||
\(908\) | −6.49567e11 | −0.0317130 | ||||||||
\(909\) | 1.10052e13 | 0.534639 | ||||||||
\(910\) | 3.45173e13 | 1.66859 | ||||||||
\(911\) | 1.67793e13 | 0.807125 | 0.403563 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403563 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(912\) | 4.13929e12 | 0.198130 | ||||||||
\(913\) | 6.58067e12 | 0.313438 | ||||||||
\(914\) | −1.18041e13 | −0.559468 | ||||||||
\(915\) | 1.20278e12 | 0.0567274 | ||||||||
\(916\) | 5.52139e11 | 0.0259131 | ||||||||
\(917\) | 1.31674e12 | 0.0614949 | ||||||||
\(918\) | 1.22441e11 | 0.00569029 | ||||||||
\(919\) | −1.49972e13 | −0.693568 | −0.346784 | − | 0.937945i | \(-0.612726\pi\) | ||||
−0.346784 | + | 0.937945i | \(0.612726\pi\) | |||||||
\(920\) | −3.68606e13 | −1.69636 | ||||||||
\(921\) | 6.46188e12 | 0.295931 | ||||||||
\(922\) | 2.31863e13 | 1.05667 | ||||||||
\(923\) | 5.84542e12 | 0.265099 | ||||||||
\(924\) | −1.29386e11 | −0.00583935 | ||||||||
\(925\) | 2.01512e13 | 0.905031 | ||||||||
\(926\) | 1.61232e13 | 0.720612 | ||||||||
\(927\) | −1.86162e12 | −0.0828004 | ||||||||
\(928\) | −1.50904e12 | −0.0667937 | ||||||||
\(929\) | 2.27528e13 | 1.00222 | 0.501111 | − | 0.865383i | \(-0.332925\pi\) | ||||
0.501111 | + | 0.865383i | \(0.332925\pi\) | |||||||
\(930\) | 4.04570e12 | 0.177346 | ||||||||
\(931\) | 1.36314e13 | 0.594658 | ||||||||
\(932\) | 1.91374e11 | 0.00830827 | ||||||||
\(933\) | 1.79857e11 | 0.00777069 | ||||||||
\(934\) | 3.05188e13 | 1.31222 | ||||||||
\(935\) | −2.15138e11 | −0.00920587 | ||||||||
\(936\) | 5.63764e12 | 0.240080 | ||||||||
\(937\) | 1.51844e13 | 0.643529 | 0.321765 | − | 0.946820i | \(-0.395724\pi\) | ||||
0.321765 | + | 0.946820i | \(0.395724\pi\) | |||||||
\(938\) | −2.49575e12 | −0.105266 | ||||||||
\(939\) | −9.92139e12 | −0.416464 | ||||||||
\(940\) | 4.12764e11 | 0.0172435 | ||||||||
\(941\) | −1.99509e13 | −0.829487 | −0.414744 | − | 0.909938i | \(-0.636129\pi\) | ||||
−0.414744 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(942\) | 1.08715e13 | 0.449841 | ||||||||
\(943\) | −4.51848e13 | −1.86076 | ||||||||
\(944\) | 3.25711e12 | 0.133493 | ||||||||
\(945\) | 1.06455e13 | 0.434235 | ||||||||
\(946\) | −7.83120e11 | −0.0317920 | ||||||||
\(947\) | −3.60211e13 | −1.45540 | −0.727700 | − | 0.685895i | \(-0.759411\pi\) | ||||
−0.727700 | + | 0.685895i | \(0.759411\pi\) | |||||||
\(948\) | −2.19012e11 | −0.00880703 | ||||||||
\(949\) | 7.12649e12 | 0.285219 | ||||||||
\(950\) | −7.09321e12 | −0.282544 | ||||||||
\(951\) | −8.67885e12 | −0.344072 | ||||||||
\(952\) | −1.21615e12 | −0.0479869 | ||||||||
\(953\) | −2.12265e13 | −0.833606 | −0.416803 | − | 0.908997i | \(-0.636849\pi\) | ||||
−0.416803 | + | 0.908997i | \(0.636849\pi\) | |||||||
\(954\) | −1.35202e13 | −0.528465 | ||||||||
\(955\) | 1.25538e13 | 0.488381 | ||||||||
\(956\) | 9.31471e11 | 0.0360669 | ||||||||
\(957\) | −4.47310e12 | −0.172387 | ||||||||
\(958\) | −3.91151e13 | −1.50037 | ||||||||
\(959\) | 2.74655e13 | 1.04859 | ||||||||
\(960\) | −2.00091e13 | −0.760339 | ||||||||
\(961\) | −2.51135e13 | −0.949844 | ||||||||
\(962\) | −2.13315e13 | −0.803032 | ||||||||
\(963\) | 1.23781e13 | 0.463807 | ||||||||
\(964\) | 5.29946e11 | 0.0197645 | ||||||||
\(965\) | −2.85867e13 | −1.06119 | ||||||||
\(966\) | 3.34935e13 | 1.23755 | ||||||||
\(967\) | −1.62338e12 | −0.0597037 | −0.0298519 | − | 0.999554i | \(-0.509504\pi\) | ||||
−0.0298519 | + | 0.999554i | \(0.509504\pi\) | |||||||
\(968\) | −2.54879e13 | −0.933029 | ||||||||
\(969\) | −1.54793e11 | −0.00564021 | ||||||||
\(970\) | 6.20551e13 | 2.25063 | ||||||||
\(971\) | −2.76845e13 | −0.999425 | −0.499712 | − | 0.866191i | \(-0.666561\pi\) | ||||
−0.499712 | + | 0.866191i | \(0.666561\pi\) | |||||||
\(972\) | −4.65206e10 | −0.00167166 | ||||||||
\(973\) | 1.84265e13 | 0.659076 | ||||||||
\(974\) | 3.69930e13 | 1.31706 | ||||||||
\(975\) | −9.91272e12 | −0.351295 | ||||||||
\(976\) | 2.10925e12 | 0.0744054 | ||||||||
\(977\) | −2.46215e13 | −0.864547 | −0.432273 | − | 0.901743i | \(-0.642288\pi\) | ||||
−0.432273 | + | 0.901743i | \(0.642288\pi\) | |||||||
\(978\) | −2.66288e12 | −0.0930738 | ||||||||
\(979\) | 1.31823e13 | 0.458637 | ||||||||
\(980\) | 1.81027e12 | 0.0626940 | ||||||||
\(981\) | 1.48749e13 | 0.512795 | ||||||||
\(982\) | 4.95061e13 | 1.69886 | ||||||||
\(983\) | 1.50739e13 | 0.514913 | 0.257456 | − | 0.966290i | \(-0.417116\pi\) | ||||
0.257456 | + | 0.966290i | \(0.417116\pi\) | |||||||
\(984\) | −2.45449e13 | −0.834609 | ||||||||
\(985\) | −3.08880e13 | −1.04551 | ||||||||
\(986\) | 1.12493e12 | 0.0379037 | ||||||||
\(987\) | 1.40179e13 | 0.470170 | ||||||||
\(988\) | 1.90695e11 | 0.00636699 | ||||||||
\(989\) | 5.14848e12 | 0.171118 | ||||||||
\(990\) | 3.21853e12 | 0.106488 | ||||||||
\(991\) | −3.48630e13 | −1.14824 | −0.574120 | − | 0.818771i | \(-0.694656\pi\) | ||||
−0.574120 | + | 0.818771i | \(0.694656\pi\) | |||||||
\(992\) | 3.55906e11 | 0.0116690 | ||||||||
\(993\) | 1.67107e13 | 0.545409 | ||||||||
\(994\) | 1.88646e13 | 0.612928 | ||||||||
\(995\) | −4.32470e12 | −0.139879 | ||||||||
\(996\) | 6.28793e11 | 0.0202461 | ||||||||
\(997\) | −3.56149e13 | −1.14157 | −0.570786 | − | 0.821099i | \(-0.693361\pi\) | ||||
−0.570786 | + | 0.821099i | \(0.693361\pi\) | |||||||
\(998\) | 4.65805e13 | 1.48634 | ||||||||
\(999\) | −6.57887e12 | −0.208981 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.b.1.7 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.7 | ✓ | 21 | 1.1 | even | 1 | trivial |